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Programmable photonic circuits performing universal linear-optical transformations underpin vital functions in photonic quantum information processing, quantum-enhanced sensor networks, machine learning, and many other intriguing applications. Recent advances in photonic integrated circuits facilitate monolithic integration of externally controlled Mach-Zehnder interferometers (MZIs) which can implement arbitrary unitary transformation on a large number of input/output modes. In this work, we demonstrate a 4×4 programmable linear photonic circuit on lithium niobate on an insulator platform employing fast, power-efficient, and low-loss electro-optical phase shifters, showing enormous advantages in terms of configuration rate and power consumption. Our device composed of cascaded MZIs possesses a total on-chip power dissipation of only 1.5 mW when operating at 100 MHz modulation rate. Our MZIs exhibit high bandwidth of 22.5 GHz, fast switching with 160-ps rise time and 120-ps fall time, low insertion loss of 0.15 dB, and on-chip extinction ratio of −34 dB for both cross and bar routes.